Press butter into a 10- x 8-inch rectangle on wax paper; chill.
Combine yeast, 1 tablespoon sugar, and water in a 2-cup liquid measuring cup; let stand 5 minutes.
Heat milk to 105° to 115°. Combine yeast mixture, warm milk, remaining 2 tablespoons sugar, 2 cups flour, and next 3 ingredients in a large mixing bowl. Beat mixture at medium speed with an electric mixer until smooth. Gradually stir in enough remaining flour to make a soft dough.
Turn dough out onto a floured surface, and knead until smooth and elastic (about 10 minutes). Place in a well-greased bowl, turning to grease top.
Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down. Cover with plastic wrap, and chill dough 1 hour.
Punch dough down; turn out onto a lightly floured surface, and roll into a 24- x 10-inch rectangle. Place chilled butter rectangle in center of dough rectangle, and carefully fold dough over butter. Pinch edges to seal.
Roll dough into an 18- x 10-inch rectangle; fold into thirds, beginning with short side. Cover and chill 1 hour.
Repeat rolling and folding procedure twice, chilling dough 30 minutes each time. Wrap dough in aluminum foil, and chill 8 hours.
Divide dough into 4 equal portions. Roll 1 portion into a 12-inch circle on a lightly floured surface, and cut into 6 wedges (keep remaining dough chilled). Roll up each wedge tightly, beginning at wide end. Place, point side down, on greased baking sheets, gently curving rolls into crescent shapes. Cover and let rise in a warm place, free from drafts, 30 minutes or until doubled in bulk.
Sprinkle dough wedges evenly with a mixture of ground cinnamon and sugar; roll up.
Bake at 425° for 8 minutes or until lightly golden. Cool croissants slightly on baking sheets, and transfer to wire racks to cool. Repeat procedure with remaining dough portions.
Combine sifted powdered sugar and milk sitrring until mixture reaches drizzling consistency. Spoon over croissants.